A tough fight. (Much like the BA/WW fight somebody dredged up again)
Despite popular misperception, Billy and Diana have comparable power in a one-on-one fight: she is nearly as strong as he is, they have equal speed (though she edges this with superior combat skills), have equal durability against blunt force attacks (though he has superior invulnerability against many other forms of attack that she, while also resistant, isn't as durable against). Her real advantage comes from her normal equipment: her lasso can subdue him, and her bracers (when used as aids in bludgeoning) and her tiara are capable of harming him in potentially serious ways (as both are capable of harming/killing gods, and have done so before).
The real *underlying* difference, however, between this fight and the one with BA/WW, is CM won't come across as someone Diana senses as evil, or needing to be killed in order to be stopped/reasoned with (and when the writer has CM's "Wisdom of Solomon" kick in, he'd sense the same thing, too). That shifts things a little, and leaves us with a 5/5 split in this case: Diana is capable of subduing CM, and he is equally capable of doing the same, even if it might take him longer on his side of the equation.